PARALLEL LINES

PARALLEL LINES

LET Subcommand

Given a line defined by two points and a third point, find the line parallel to the first line and containing the third point.

LET <yout> <xout>= PARALLEL LINES <x1> <y1> <x2> <y2> <x3> <y3>
                        <SUBSET/EXPCEPT/FOR qualification>
where <x1> is a variable or parameter containing the x-coordinates for the first point of line one;
            <y1> is a variable or parameter containing the y-coordinates for the first point of line one;
            <x2> is a variable or parameter containing the x-coordinates for the second point of line one;
            <y2> is a variable or parameter containing the y-coordinates for the second point of line one;
            <x3> is a variable or parameter containing the x-coordinates for the third point;
            <y3> is a variable or parameter containing the y-coordinates for the third point;
            <yout> is a variable containing the y-coordinates of the second point of the parallel line;
            <xout> is a variable containing the x-coordinates of the second point of the parallel line;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET YOUT XOUT = PARALLEL LINES X1 Y1 X2 Y2 X3 Y3 X4 Y4

None

None

PERPINDICULAR LINE	= Determine the coordinates for a point that defines a perpindicular line determined by a point and a line defined by two points.
ANGRAD	= Return the counter clockwise angle, in radians, of the angle determined by three points.
DPNTLINE	= Compute the perpindicular distance between a point and a line defined by a point and a slope.
POINTS IN POLYGON	= Determine whether points are in the interior of a convex polygon.
CONVEX HULL	= Determine the convex hull of a set of points.
TRANSFORM POINTS	= Perform location, scale, and rotation transformation for a set of points.
EXTREME POINTS	= Determine the extreme points of a set of points.
LINE INTERSECTIONS	= Determine the intersection points for a set of lines.

Computational Geometry

2012/10

 
dimension 40 columns
skip 25
read convhull.dat x y
.
let y2 x2 = 2d convex hull y x
let xtemp = x2(1)
let ytemp = y2(1)
let y2 = combine y2 ytemp
let x2 = combine x2 xtemp
let x3 = x2
let y3 = y2
let n = size y2
let nm1 = n - 1
retain x2 y2 for i = 1 1 nm1
retain x3 y3 for i = 2 1 n
let slope = slope(x2,y2,x3,y3)
let pdist = dpntline(xtemp,ytemp,x3,y3,slope)
let xtempv = xtemp for i = 1 1 nm1
let ytempv = ytemp for i = 1 1 nm1
let y5 x5 = parallel line x2 y2 x3 y3 xtempv ytempv
.
set write decimals 4
print "Anchor Point: (^xtemp,^ytemp)"
print " "
print " "
print x2 y2 x3 y3 x5 y5
    

The following output is generated

 
Anchor Point: (0,-2.)
 
 
 
------------------------------------------------------------------------------------------
             X2             Y2             X3             Y3             X5             Y5
------------------------------------------------------------------------------------------
         0.0000        -2.0000         1.0000        -1.7300         0.0000        -2.0000
         1.0000        -1.7300         1.7300        -1.0000         1.0000        -1.7300
         1.7300        -1.0000         2.0000         0.0000         1.7300        -1.0000
         2.0000         0.0000         1.7300         1.0000         2.0000         0.0000
         1.7300         1.0000         1.0000         1.7300         1.7300         1.0000
         1.0000         1.7300         0.0000         2.0000         1.0000         1.7300
         0.0000         2.0000        -1.0000         1.7300         0.0000         2.0000
        -1.0000         1.7300        -1.7300         1.0000        -1.0000         1.7300
        -1.7300         1.0000        -2.0000         0.0000        -1.7300         1.0000
        -2.0000         0.0000        -1.7300        -1.0000        -2.0000         0.0000
        -1.7300        -1.0000        -1.0000        -1.7300        -1.7300        -1.0000
        -1.0000        -1.7300         0.0000        -2.0000        -1.0000        -1.7300